A. I. Bufetov, B. M. Gurevich, “Existence and uniqueness of the measure of maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials”, Sb. Math., 202:7 (2011), 935

Sbornik: Mathematics

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Sbornik: Mathematics, 2011, Volume 202, Issue 7, Pages 935–970
DOI: https://doi.org/10.1070/SM2011v202n07ABEH004172 (Mi sm7739)

This article is cited in 17 scientific papers (total in 17 papers)

Existence and uniqueness of the measure of maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials

A. I. Bufetov^ab, B. M. Gurevich^cd

^a Steklov Mathematical Institute, Russian Academy of Sciences
^b Department of Mathematics, Rice University, Houston, TX, USA
^c M. V. Lomonosov Moscow State University
^d A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

English version PDF (549 kB) Citations (17) Russian version article

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DOI: https://doi.org/10.1070/SM2011v202n07ABEH004172

Abstract: The main result of the paper is the statement that the ‘smooth’ measure of Masur and Veech is the unique measure of maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials. The proof is based on the symbolic representation of the flow in Veech's space of zippered rectangles.
Bibliography: 29 titles.

Keywords: moduli space, Rauzy induction, symbolic dynamics, Markov shift, suspension flow.

Received: 13.05.2010 and 21.11.2010

Bibliographic databases:

Document Type: Article

UDC: 517.938

MSC: 28D20, 37A35, 37D, 37E35

Language: English

Original paper language: Russian

Citation: A. I. Bufetov, B. M. Gurevich, “Existence and uniqueness of the measure of maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials”, Sb. Math., 202:7 (2011), 935–970

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm7739

https://doi.org/10.1070/SM2011v202n07ABEH004172

https://www.mathnet.ru/eng/sm/v202/i7/p3

This publication is cited in the following 17 articles:

Buzzi J., Crovisier S., Sarig O., “Measures of Maximal Entropy For Surface Diffeomorphisms”, Ann. Math., 195:2 (2022), 421–508
Bufetov I A., Solomyak B., “Holder Regularity For the Spectrum of Translation Flows”, J. Ecole Polytech.-Math., 8 (2021), 279–310
Kucherenko T., Thompson D.J., “Measures of Maximal Entropy For Suspension Flows Over the Full Shift”, Math. Z., 294:1-2 (2020), 769–781
Iommi G., Riquelme F., Velozo A., “Entropy in the Cusp and Phase Transitions For Geodesic Flows”, Isr. J. Math., 225:2 (2018), 609–659
Eskin A., Mirzakhani M., “Invariant and Stationary Measures For the Sl(2, R) Action on Moduli Space”, Publ. Math. IHES, 2018, no. 127, 95–324
Climenhaga V., “Specification and Towers in Shift Spaces”, Commun. Math. Phys., 364:2 (2018), 441–504
Alexander I. Bufetov, Boris Solomyak, “The Hölder property for the spectrum of translation flows in genus two”, Israel J. Math., 223:1 (2018), 205–259
Aimino R., Nicol M., Todd M., “Recurrence Statistics For the Space of Interval Exchange Maps and the Teichmüller Flow on the Space of Translation Surfaces”, Ann. Inst. Henri Poincare-Probab. Stat., 53:3 (2017), 1371–1401
A. Avila, P. Hubert, A. Skripchenko, “Diffusion for chaotic plane sections of 3-periodic surfaces”, Invent. Math., 206:1 (2016), 109–146
B. M. Gurevich, “A lower estimate of the entropy of an automorphism and maximum entropy conditions for and invariant measure of a suspension flow over a Markov shift”, Dokl. Math., 91:2 (2015), 186–188
B. Gurevich, “On a measure with maximal entropy for a suspension flow over a countable alphabet Markov shift”, Eur. J. Math., 1:3 (2015), 545–559
Godofredo Iommi, Thomas Jordan, Mike Todd, “Recurrence and transience for suspension flows”, Isr. J. Math., 209:2 (2015), 547
G. Iommi, Th. Jordan, “Phase transitions for suspension flows”, Commun. Math. Phys., 320:2 (2013), 475–498
A. I. Bufetov, “Limit theorems for suspension flows over Vershik automorphisms”, Russian Math. Surveys, 68:5 (2013), 789–860
A. Bufetov, “Limit theorems for translation flows”, Ann. Math., 179:2 (2013), 431–499
U. Hamenstädt, “Bowen's construction for the Teichmüller flow”, J. Mod. Dyn., 7:4 (2013), 489–526
Climenhaga V., Thompson D.J., “Intrinsic ergodicity beyond specification: $\beta$ -shifts, $S$ -gap shifts, and their factors”, Israel J. Math., 192:2 (2012), 785–817

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	1119
Russian version PDF:	280
English version PDF:	28
References:	102
First page:	52

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